“Universal credit is working,” he said. “So I can confirm that the rollout will continue, and to the planned timetable.

“We’re not going to rush things; it is more important to get this right than to do this quickly, and this won’t be completed until 2022. But across the country, we will continue to transform our welfare system to further support those who aspire to work.”

Gauke said the government would be “refreshing the guidance” to staff at the Department for Work and Pensions (DWP) over the possibility of giving advance payments to claimants in difficulty.

“Claimants who want an advance payment will not have to wait six weeks, they will receive this advance within five working days,” Gauke said. “And if someone is in immediate need, then we fast-track the payment, meaning they will receive it on the same day.”

Debbie Abrahams, the shadow work and pensions secretary, condemned the confirmation of the rollout, saying Gauke “should immediately end the misery caused by the six-week wait for payment of universal credit”.

Charities and campaign groups also expressed concern. Child Poverty Action Group said it welcomed the government being more proactive on advance payments, but its chief executive, Alison Garnham, said: “Given the serious and wide-ranging concerns about nearly every aspect of universal credit, we had hoped for more on how the government plans to address the funding, policy design and administrative problems plaguing universal credit before it is rolled out to families.”

Gillian Guy, the chief executive of Citizens Advice, said it was good that Gauke had recognised there were problems. “However, we are disappointed he has not taken this opportunity to pause the rollout to ensure the problems are fixed before it speeds up significantly.

“Evidence from Citizens Advice and others – including the DWP itself – shows many people risk getting into serious debt as a result of delayed first payments. Advance payments can help people make ends meet during this period, but they must be combined with more action to reduce the number of people waiting more than six weeks for their initial payment.”

Speaking earlier on Monday, Allen said she and 14 other Conservative MPs, two more than originally reported, had written to the government calling for the rollout to be paused.

“My understanding is there isn’t any legislation that might stop or start this, it is already in train. It is more a question of whether it reflects what we heard the prime minister say when she first became PM on the steps of No 10,” Allen told BBC Radio 4’s Today programme.

“She showed to me a really clear understanding of people who are struggling to make ends meet.

“So to me, it doesn’t fit with that belief in a moral compass. These are the vulnerable people with no recourse to savings. We should be supporting them, because universal credit is about supporting people in work and helping them move up the working ladder and take on more hours. That is who we should, as Conservatives, be supporting.”

Allen’s comments came after the former government official Dame Louise Casey, who conducted a year-long study for ministers into community cohesion, likened pressing ahead with the universal credit rollout to “jumping over a cliff”.

She told BBC Radio 4’s PM programme on Friday that the changes, which involve merging six benefits into a single monthly payment, made her “hair stand on end”.

Casey, who led the rough sleepers unit under Tony Blair’s Labour government, said the plans, which have been tried on 530,000 claimants, would “end up making the situation worse for people that are working poor, let alone people that are on benefits”.

The Labour MP Frank Field, who chairs the work and pensions select committee, said: “David Gauke has today pressed the button that will cause havoc to hundreds of thousands of poorer people’s lives, building up to a meltdown over Christmas.

“It is not too late for him to act politically wisely, as well as compassionately. People must be put before arbitrary rollout dates of a project which cannot work.”